how do these fraction reduce to the lowest terms

4/9-1/9= 3/9=1/3

a+7/a-4+9-5a/a-4=

3/x+1+2/x-1=

2/x-3 + 3/x-3

1/9+1/3x over x/9-1/x=

solve the equation

-3/x=x/-3

x/3 =4/x+1=

5/y-3 = y+7/2y-6 +1=

How far back do we have to go to explain this?

Do you know how to calculate least common denominators?

Do you know how to break a number down into its prime number factors?

Do you know that adding the same quantity to both sides of a equation results in a new equation that is just as true as the original, even if the quantity is a product of a variable (like 5x)? Do you know that the same is true for multiplication and division?

Do you now how few quantities are equal to their reciprocal?